Five Really Simple, Useful and Free Retirement Formulas

Here are five great, simple little formulas for retirement planning -- all of which are not, you'll notice, the 4% rule. Retirement planning can often be complex if not a completely unanswerable problem domain or as Wade Pfau once opined: "A truly safe withdrawal rate is unknown and unknowable". On the other hand, by using some simple, deterministic formulas to wrap your head around what might or might not work before you get into the deep weeds with a planner and his or her complex, proprietary models I think you can, if not necessarily DIY, at least save a little time and money and make the conversations-to-come more efficient. Moshe Milevsky, in a great article on de-emphasizing complex simulator-based retirement ruin calculations (It’s Time to Retire Ruin (Probabilities) ), points out the pros and big cons of stochastic modeling (e.g., simulators). He tells us, helpfully, that "the highly technical and subtle stochastic 2.0 lecture makes no sense until the deterministic 1.0 lecture is crystal clear." This just means walk with simple formulas before you run with a heavy duty model. So this post is part of the 1.0-walk "lecture." In my mind, some of the benefits of starting with the deterministic 1.0 level include:

• It's free and not all that hard
• It provides a degree or two of (current and future) freedom from advisors and planners and throws a healthy dose of control into your own hands
• It provides, if you are willing, a good self-directed tutorial on some of the most gnarly core assumptions you need to make, especially when you really spend some time thinking about them. For example, think about the "expected real rate of return" for a minute; there is a lot that goes into that number and it is always a good conversation to have, especially in 2016
• With simple formulas one can also, for a brief blissful moment, steer widely clear of the large number of buried, invisible assumptions and biases of modelers and programmers and advisors that are implicit in advisor provided software (or even the free ones on the internet for that matter)
• Used in concert, multiple formulas and techniques provide informative context and multiple points of view in the planning process. It can set the stage for more complicated planning and discussions later
• Since planning, in its heart of hearts, is or should be a continuous process, you now have an entry level tool-set at your disposal to that will allow you to adapt to changing circumstances at your leisure. My mental model here is skiing: try to ski without being aware of changing terrain and without adjusting your speed, direction, and where you are looking based on everything that is going on around you…and you will get hurt. Stay aware, in other words.

FIVE SIMPLE FORMULAS

1. Portfolio Longevity Using Milevsky's Fibonacci Formula

This is the formula that Moshe Milevsky -- using a formula that originated from Leonardo Fibonacci in the 1100s and that was created to figure out how long money would last given spend and growth assumptions -- suggests using to frame a discussion between advisor & client. His reasoning is that it can start a more constructive conversation around retirement than a simulator can do...that is, before someone understands the pros and cons and subtleties and assumptions of simulators. It also focuses the conversation on a small number of important variables like the growth rate.

EL        estimated portfolio longevity

M         nest egg (money)

w         withdrawal rate in dollars per year

g          annual real growth rate of portfolio as a %. It should also be

            net of fees, taxes, and maybe market risk. Much of the constructive
           discussion, in an advisory conversation, will revolve around g

Output is the number years the portfolio will last given the inputs. Then compare that result to what you might expect for your average, long, and then longest terminal retirement ages in your plan. Note that the formula doesn't work that well if you happen to spend less than you earn. I'm thinking that is closer to a perpetuity in which case you are in pretty good shape and probably don't need a formula (or blog post) like this.

2. Spend Rate Using the Excel PMT Function

Excel is Excel of course but the PMT function, an ever useful thing, was recently mentioned in an article by M. Barton Waring and Laurence B. Siegel (The Only Spending Rule Article You’ll Ever Need) who used it to create a retirement spending rule they called ARVA (Annually Recalculated Virtual Annuity). Enter the simple assumptions into the formula and then repeat that process each year. If you can spend what it says, you'll likely never run out of money. Like the Milevsky formula this has the benefit of incredible simplicity (ignore the spending volatility it implies for now). It also tends to focus the discussion on the growth rate assumption. It is also free. Depending on the person you are talking to, it is sometimes called the mortgage formula or an annuity formula.  It also happens to be more or less the same math as the previous formula but turned inside out; it's solving for P rather than n.

PMT(r,n,Pv) in Excel

or

P = ( Pv * r )  / [ 1 - (1 + r)^-n ]

P          the "payment" or spend rate estimate

r           annual real growth rate; g in the previous formula

n          number of retirement years expected (I use 95 minus my age but 30 is often used)

Pv        money or nest egg or endowment

Output is the estimated spend rate for this year.  W&S recommend doing all again next year because, well because everything changes.  Technically things change continuously but a continuous recalc might be a little OCD.  Playing around with it doesn't hurt anyone, though.

3. Blanchett's Two Simple Spending Formulas

Based on a whole pile of research and a bunch of Monte Carlo simulations, David Blanchett derived a rule of thumb formula (or formulas) that allows one to get results pretty close to what a simulator might generate for successful retirement spending rates…that is if one does not happen to have a simulator [article here]. It seems to work pretty well from my own look-see. He found that one formula does not work for all ages, though. The first formula (Dynamic) apparently works better for periods that are 15 years or more and the second (RMD Approach) is better for periods 15 years or less.

A. Dynamic Formula for Retirements >= 15 Years

w                     withdrawal rate

Years               distribution period

PoS                  target probability of success

Alpha               fees as a negative percent like -00.50%

Equity%           equity allocation

Output is a proxy for a simulator-generated suggested retirement withdrawal rate for the given input variables and a target success rate. Designed more for advisors than retail investors, this is not as hard as it looks for self-managing retirees.

 B. RMD Approach for Retirements <= 15 years

Blanchett says that the equation is based on the IRS’ required minimum distribution (RMD) and works better for short retirements (with respect to the underlying simulator results) than the previous formula.  See the article for his rationale

w% _{[<=15 years]}  =  1 / Years

w                     withdrawal rate

Years               distribution period

Output is withdrawal rate percent for a short retirement. 

4. Divide by 20 Rule of Thumb

I've already written more than I probably need to on this slick little rule (here). This rule was created by Evan Inglis and is a rule of thumb designed to calculate a simple "safe" retirement spend rate on an age-adjusted basis. The purpose of the rule is, I gather, to be: a) simple, b) conservative and relatively safe but not foolproof, c) age adjusted, d) get spending pretty close to a reasonable level of expected real returns, and e) more than likely leave a little bequest if you last long enough. Seems to work pretty well as far as I can see.

w = Age / 20

w         withdrawal rate percentage for a given year/age

Age      age

20        this rule of thumb number is a range boundary. That means that below 20 is more than likely pretty safe; above 10 is pretty dangerous.  After about age  70 "20" might get a little conservative and will either tend to leave a legacy or perhaps it can be adjusted to something else like divide by 18 or 19 or 17…

Output of this formula is a withdrawal rate percent for spending in a given year for a given age.

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I will add more formulas here as I run into them or as they are sent to me…

Just for fun also see: Simple vs Complex by Josh Brown